Group actions on spaces of rational functions

Let Hold be the space consisting of all holomorphic maps f : S 2 → S 2 of degree d. The group Hol1 = PSL2( ) acts on Hold freely by the post-composition and we shall study the orbit space Xd = Hol1\Hold. As an application we shall determine the homotopy types of the universal covering spaces of Hold and Xd explicitly.